Transmission, refraction and dark-field retrieval in hard X-ray grating interferometry

Abstract

A three‐image algorithm is proposed to retrieve the sample's transmission, refraction and dark‐field information in hard X‐ray grating interferometry. Analytical formulae of the three‐image algorithm are theoretically derived and presented, and evaluated by proof‐of‐principle synchrotron radiation experiments. The results confirm the feasibility of the proposed algorithm. The novelty of the proposed algorithm is that it allows versatile and tunable multimodal X‐ray imaging by substantially relaxing the existing limitations on the lateral grating position. Furthermore, this algorithm can also be adapted for samples with negligible refraction, reducing the number of required sample measurements to two. Furthermore, the noise properties of the retrieved images are investigated in terms of the standard deviations. Theoretical models are presented and verified by synchrotron radiation measurements. It is shown that the noise standard deviations exhibit strong dependence on the lateral grating position, especially in the case of refraction and dark‐field images. Further noise reduction and dose reduction can thus be possible by optimizing the lateral grating position for a selected region of interest. Those results can serve as general guidelines to optimize the data acquisition scheme for specific applications and problems.

Quantitative coherence analysis of dual phase grating x-ray interferometry with source grating*

“…A high fringe visibility is always required to achieve a high signal-to-noise ratio (SNR) in x-ray grating-based interferometry. [17,18,33,34] As shown in Eq. ( 10), the visibility of those resolvable intensity fringes is dependent on the x-ray spectrum, the setup geometry, the Fourier coefficients of the source grating and dual phase gratings, and the ratio p 1 /p 2 .…”

“…Over the last two decades, x-ray grating interferometry has attracted increasing attention from the scientific community. [1][2][3][4][5][6][7][8][9][10][11][12][13][15][16][17][18] As a multi-modal imaging technique, x-ray grating interferometry provides simultaneously three complementary signals, i.e., attenuation, refraction, and darkfield, from the same set of experimental data. [1][2][3][4]11,18] Particularly, standard x-ray tubes are fully compatible with x-ray grating interferometers in the so-called Talbot-Lau geometry.…”

“…Analyzing the local distortion of the interference pattern allows one to retrieve the x-ray attenuation, refraction, and dark-field signals on a pixel-by-pixel basis. [1][2][3][4]11,17] In order to achieve a high sensitivity, the phase grating typically has a period of a few micrometers. The resulting interference fringes, with a pitch of several micrometers, cannot be directly resolved by common imaging detectors with a typical pixel size of several tens of micrometers.…”